Abstract
A charged isolated particle with spherically symmetry is considered at origin in empty space. The particle has both mass and charge; therefore it is under the influence of both gravitational and electro-magnetic field. So to find out a line element especial attention is given in Einstein’s gravitational and Maxwell’s electro-magnetic field equations. Initially Einstein’s field equations are considered individually for gravitational and electro-magnetic fields in empty space. In this work initially starts with Schwarzschild like solution and then a simple elegant, systematic method is used. In these methods the e-m field tensor is also used from Maxwell’s electro-magnetic field equations. Finally thus a new metric is found for both positive and negative charged particles. The new metric for electron is not same as the metric is devised by Reissner and Nordstrom. The new metric for proton is used to find another new metric for rotating charged particle. The new metric is extended for the massive body and gives us some new information about the mass required to stop electro-magnetic interaction. It gives interesting information that planet having mass more than 1.21 times of Jupiter mass, live cannot survive. Also gives information that the mass greater than the aforesaid mass there is no electrically charged body in the universe.
Highlights
Einstein’s field equations [1] are a set of nonlinear differential equations, so these equations are difficult to find the exact analytical solution
Schwarzschild metric was understood to describe a black hole [16] in the year 1958 and Kerr [3, 17] generalised the solution for rotating black hole in the year 1963
To find out the value of B let we first find out an equation of motion of a particle [26] with very low velocity in static field, and we find the e-m field tensor [26] and find out the value of B
Summary
Einstein’s field equations [1] are a set of nonlinear differential equations, so these equations are difficult to find the exact analytical solution. T Kaluza [9] in 1921 and later Oskar Klein [10, 11] in 1926 try to solve the relativity as a geometrical theory of gravitation and electro-magnetic (e-m) field. The gravitational field due to an isolated electron was given by Reissner [12, 13] and Gunner Nordstrom [14] in 1921 and later by G. Schwarzschild metric was understood to describe a black hole [16] in the year 1958 and Kerr [3, 17] generalised the solution for rotating black hole in the year 1963. Newman [18, 19] try to describe the metric for charged, rotating body on the basis of Reissner-Nordstrom solution in the year 1965. A brief introduction is given here about Schwarzschild, ReissnerNordstrom, Kerr and Newman metrics
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